Prism (EntityClass, 5)

From Hi.gher. Space

(Difference between revisions)
m (Redirecting to Formable shape#Prism)
Line 1: Line 1:
-
#redirect [[Formable shape#Prism]]
+
<[#ontology [kind class] [cats Construction Shape]]>
 +
A '''prism''' is a shape which has been constructed by [[extrusion]].
 +
 
 +
There is a simple relationship between the numbers of [[element]]s of a prism, and the numbers of elements of its base:
 +
<blockquote>''H''<sub>''n''</sub>(+A) = 2''H''<sub>''n''</sub>(A) + ''H''<sub>''n-1''</sub>(A)</blockquote>
 +
where ''H''<sub>''n''</sub>(X) is the number of ''n''-dimensional elements of the shape X, A is the base shape and +A is the prism.
 +
 
 +
The first term in the RHS of this equation corresponds to the elements of the base that get duplicated and form the "ends" of the prism, and the second term corresponds to the elements that get extruded (and hence are also prisms) and form the "sides" of the prism.

Revision as of 15:35, 11 March 2011

A prism is a shape which has been constructed by extrusion.

There is a simple relationship between the numbers of elements of a prism, and the numbers of elements of its base:

Hn(+A) = 2Hn(A) + Hn-1(A)

where Hn(X) is the number of n-dimensional elements of the shape X, A is the base shape and +A is the prism.

The first term in the RHS of this equation corresponds to the elements of the base that get duplicated and form the "ends" of the prism, and the second term corresponds to the elements that get extruded (and hence are also prisms) and form the "sides" of the prism.

Pages in this category (7)